Physically Motivated Models for Heterogeneous Random Phenomena

Abstract

In 2010, Tunde Ogunnaike published the book Random Phenomena, a comprehensive introduction to the physically based modeling of random phenomena for engineers. This paper is primarily a survey of concepts and methods for dealing with more complex heterogeneous random phenomena not addressed in Random Phenomena, but building on the foundation that the book establishes. Specifically, this paper discusses three extensions of that material: discrete mixture models, extensions of the linear regression models discussed in Random Phenomena (generalized linear models for strongly non-Gaussian response variables, and mixtures of regression models), and an extension of the Central Limit Theorem that is believed to be new. Since, as Random Phenomena emphasizes, software is necessary for analyzing and modeling random data, procedures in the open-source R programming environment are described that support all of the concepts and methods presented here.